Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.
Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.
Abstract Drawing inspiration from the physical Ising model, optical Ising machines have emerged as a promising paradigm in optical computing. These machines typically utilize optical phase or amplitude modulators to represent the analog spin variables, which determine the final Hamiltonian by the combinatorial configuration of the complex optical field. However, current optical modulators exhibit relatively low modulation resolution and significant technical challenges arise when scaling up optical Ising systems to maintain consistent performance across integrated device clusters. Here we propose a programmable optical differential Ising machine that provides direct access to changes in the Hamiltonian. This system streamlines unnecessary matrix calculations, thereby reducing the requirements for the size and precision of the modulator matrix. Through numerical simulations on 60 to 100 spin MaxCut benchmark problems, we determine that the minimum required resolutions for the DAC and ADC are 6 bits and 5 bits, respectively, along with a significant tolerance of 0.3 rad for phase errors and over 10 multiplexing operations. Additionally, 100-spin experiments with a dual-channel system demonstrate its potential for phase transition simulation and solving complex optimization challenges.
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the advantages of high speed and parallelism, enabling efficient hardware acceleration for finding ground-state solutions to combinatorial optimization problems. In this work, we demonstrate a novel programmable photonic Ising solver based on a hexagonal mesh general-purpose programmable photonic platform. The integrated system allows reconfigurable matrix multiplication and computes the Hamiltonian iteratively using an annealing algorithm that facilitates spin updates and effectively searches for the ground state. As a proof of concept, we experimentally solve two benchmark optimization problems, a fundamental three-node ferromagnetic coupling problem with external bias that demonstrates nontrivial spin interactions, and a four-node Max-Cut problem with arbitrary coupling matrices. Furthermore, to establish a large-scale capability, we emulated Ising problems with sizes up to N = 50, achieving success probabilities exceeding 80\%. Additionally, we examined the impact of errors, such as phase and coupling, on the performance of the programmable photonic Ising machine. Our general-purpose photonic Ising machine paves the way for implementing large-scale, programmable architectures for solving optimization problems.
Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.
Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields, reducing either speed or spin count. We demonstrate an amplitude-only, rank-free spatial photonic Ising machine in which arbitrary Ising Hamiltonians are encoded as Hadamard products on aligned amplitude and binary spatial modulators and read out by a single-pixel intensity measurement. The machine directly programs fully connected 797-spin Ising models with external fields at nearly 9-bit precision and operates at a constant iteration rate of ~200 Hz. By removing zero-valued product terms, the same architecture scales to sparse problems and experimentally solves a Max-Cut instance on a 424,108-vertex Mobius ladder graph. We also observe the phase transition of the Sherrington-Kirkpatrick model, demonstrating programmable optical simulation beyond low-rank couplings. These results establish amplitude modulation as a scalable route to programmable photonic Ising machines.
Abstract Optical Ising machines have emerged as a promising dynamical hardware solver for computational hard optimization problems. These Ising machines typically require an optical modulator to represent the analog spin variables of these problems. However, modern day optical modulators have a relatively low modulation resolution. We therefore investigate how the low bit-resolution of optical hardware influences the performance of this type of computing platform. Based on numerical simulations, we determine the minimum required bit-resolution of an optical Ising machine for different benchmark problems of different sizes. Our study shows that a limited bit-resolution of 8bit is sufficient for the optical modulator. We also observe that the use of a 1bit-resolution modulator significantly improves the performance of the Ising machine across all considered benchmark problems.
Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale OIM/OPMs, leveraging the advantages of digital computing to offer high precision, programmability, and scalability. The performance of the proposed GPU framework is evaluated on the max-cut problems from the GSET benchmark dataset and graph coloring problems from the SATLIB benchmarks dataset, demonstrating competitive speed and accuracy in tackling large-scale problems. The results from simulations, reaching up to 11295x speed-up over CPUs with up to 99% accuracy, establish this framework as a scalable, massively parallelized, and high-fidelity digital realization of OIM/OPMs.